### Theory:

To subtract two trinomials, you must:

1) remove the brackets and change the signs of the trinomials that are preceded by the sign "$$-$$" to the opposite;
2) combine the like terms of the trinomials.
Example:
Let us calculate the difference of trinomials $\left(7{x}^{2}+3x-2\right)$ and $-2{x}^{2}+2x+3$

1) Write down the difference of the trinomials and remove the brackets, taking the signs before the brackets into account:

$\left(7{x}^{2}+3x-2\right)-\left(-2{x}^{2}+2x+3\right)=7{x}^{2}+3x-2+2{x}^{2}-2x-3$

2) Find the like terms:

$\underset{¯}{7{x}^{2}}+\underset{¯}{\underset{¯}{3x}}-\underset{⏟}{2}+\underset{¯}{2{x}^{2}}-\underset{¯}{\underset{¯}{2x}}-\underset{⏟}{3}$

3) Combine the like terms:

$\underset{¯}{7{x}^{2}}\phantom{\rule{0.147em}{0ex}}\underset{¯}{\underset{¯}{+3x}}-2\underset{¯}{+2{x}^{2}}\phantom{\rule{0.147em}{0ex}}\underset{¯}{\underset{¯}{-2x}}-3=\left(7+2\right){x}^{2}+\left(3-2\right)x-2-3=9{x}^{2}+1x-5$

4) If the coefficient of a term is $$1$$, then usually we do not write it:

$9{x}^{2}+1x-5=9{x}^{2}+x-5$
Important!
Remember: the sum or the difference of trinomials is always a trinomial.
To find the opposite of a trinomial, change the signs of the coefficients of all terms to the opposite.
Example:
The opposite of
$-2{m}^{2}n+3\mathit{mn}-4$ is
$2{m}^{2}n-3\mathit{mn}+4$

The opposite of
$7{a}^{2}-2,5a-8$ is
$-7{a}^{2}+2,5a+8$

The opposite of
${x}^{n}-0,05$ is
$-{x}^{n}+0,05$
Two trinomials are called opposite if their sum is $$0$$.
Example:
Trinomials $-4{a}^{2}b+3\mathit{ab}+2$ and $4{a}^{2}b-3\mathit{ab}-2$ are opposite, because their sum is zero:

$\left(-4{a}^{2}b+3\mathit{ab}+2\right)+\left(4{a}^{2}b-3\mathit{ab}+-2\right)=$

$\begin{array}{l}-\overline{)4{a}^{2}b}+3\mathit{ab}+2+\overline{)4{a}^{2}b}-3\mathit{ab}-2=\\ \\ =\overline{)3\mathit{ab}}+2-\overline{)3\mathit{ab}}-2=\overline{)2}-\overline{)2}=0\end{array}$